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Advances in Mathematical Physics
Volume 2018, Article ID 1570407, 13 pages
Research Article

Higher Approximations to Study Statistical Characteristics of Waves in Multiscale Inhomogeneous Media

Irkutsk State University, 20 Gagarin Blvd, Irkutsk 664003, Russia

Correspondence should be addressed to M. V. Tinin; ur.usi.ipa@ninitm

Received 29 April 2017; Accepted 4 January 2018; Published 7 February 2018

Academic Editor: Xavier Leoncini

Copyright © 2018 M. V. Tinin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The previously obtained integral field representation in the form of double weighted Fourier transform (DWFT) describes effects of inhomogeneities with different scales. The first DWFT approximation describing the first-order effects does not account for incident wave distortions. However, in inhomogeneous media the multiscale second-order effects can also take place when large-scale inhomogeneities distort the field structure of the wave incident on small-scale inhomogeneities. The paper presents the results of the use of DWFT to derive formulas for wave statistical moments with respect to the first- and second-order effects. It is shown that, for narrow-band signals, the second-order effects do not have a significant influence on the frequency correlation. We can neglect the contribution of the second-order effects to the spatial intensity correlation when thickness of the inhomogeneous layer is small, but these effects become noticeable as the layer thickness increases. Accounting for the second-order effects enabled us to get a spatial intensity correlation function, which at large distances goes to the results obtained earlier by the path integral method. This proves that the incident wave distortion effects act on the intensity fluctuations of a wave propagating in a multiscale randomly inhomogeneous medium.